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This second special issue devoted to ‘developments in computational models’ (the first was Volume 16 Issue 4) came out of an open call for papers following the First International Workshop on Developments in Computational Models (DCM). This took place in Lisbon, Portugal, on the 10th July 2005, and was a satellite event of ICALP 2005 focused on abstract models of computation and their associated programming paradigms.

We define BACI(Boxed Ambients with Communication Interfaces), an ambient
calculus with a flexible communication policy. Traditionally, typed ambient
calculi have a fixed communication policy determining the kind of information
that can be exchanged with a parent ambient, even though mobility changes the
parent. BACI lifts that restriction, allowing different
communication policies with different parents during computation. Furthermore,
BACI separates communication and mobility by making the
channels of communication between ambients explicit. In contrast with other
typed ambient calculi where communication policies are global, each ambient in
BACI is equipped with a description of the communication
policies ruling its information exchange with parent and child ambients. The
communication policies of ambients increase when they move: more precisely, when
an ambient enters another ambient, the entering ambient and the host ambient can
exchange their communication ports and agree on the kind of information to be
exchanged. This information is recorded locally in both ambients.

We show the type-soundness of BACI, proving that it satisfies the
subject reduction property, and we study its behavioural semantics by means of a
labelled transition system.

We extend the coalgebraic account of specification and refinement of objects and classes in object-oriented programming given by Reichel and Jacobs to (generalised) binary methods. These are methods that take more than one parameter of a class type. Class types include products, sums and powerset type constructors. To allow for class constructors, we model classes as bialgebras. We study and compare two solutions for modelling generalised binary methods, which use purely covariant functors.

In the first solution, which applies when we already have a class implementation, we reduce the behaviour of a generalised binary method to that of a bunch of unary methods. These are obtained by freezing the types of the extra class parameters to constant types. If all parameter types are finitary, the bisimilarity equivalence induced on objects by this model yields the greatest congruence with respect to method application.

In the second solution, we treat binary methods as graphs instead of functions, thus turning contravariant occurrences in the functor into covariant ones.

We present a simple module calculus where selection and execution of a component is possible on open modules, that is, modules that still need to import some external definitions. Hence, it provides a kernel model for a computational paradigm in which standard execution (that is, execution of a single computation described by a fragment of code) can be interleaved with operations at the meta-level, which can manipulate in various ways the context in which this computation takes place. Formally, this is achieved by introducing configurations as basic terms. These are, roughly speaking, pairs consisting of an (open, mutually recursive) collection of named components and a term representing a program running in the context of these components. Configurations can be manipulated by classical module/fragment operators, hence reduction steps can be either execution steps of the program or steps that perform module operations (called reconfiguration steps).

Since configurations combine the features of lambda abstractions (first-class functions), records, environments with mutually recursive definitions and modules, the calculus extends and integrates both traditional module calculi and recursive lambda calculi. We state confluence of the calculus, and propose different ways to prevent errors arising from the lack of some required component, either by a purely static type system or by a combination of static and run-time checks. Moreover, we define a call-by-need strategy that performs module simplification only when needed and only once, leading to a generalisation of call-by-need lambda calculi that includes module features. We prove the soundness and completeness of this strategy using an approach based on information content, which also allows us to preserve confluence, even when local substitution rules are added to the calculus.

In this paper we discuss the following interesting question about accepting hybrid networks of evolutionary processors (AHNEP), which are a recently introduced bio-inspired computing model. The question is: how many processors are required in such a network to recognise a given language L? Two answers are proposed for the most general case, when L is a recursively enumerable language, and both answers improve on the previously known bounds. In the first case the network has a number of processors that is linearly bounded by the cardinality of the tape alphabet of a Turing machine recognising the given language L. In the second case we show that an AHNEP with a fixed underlying structure can accept any recursively enumerable language. The second construction has another useful property from a practical point of view as it includes a universal AHNEP as a subnetwork, and hence only a limited number of its parameters depend on the given language.

A restriction category is an abstract formulation for a category of partial maps, defined in terms of certain specified idempotents called the restriction idempotents. All categories of partial maps are restriction categories; conversely, a restriction category is a category of partial maps if and only if the restriction idempotents split. Restriction categories facilitate reasoning about partial maps as they have a purely algebraic formulation.

In this paper we consider colimits and limits in restriction categories. As the notion of restriction category is not self-dual, we should not expect colimits and limits in restriction categories to behave in the same manner. The notion of colimit in the restriction context is quite straightforward, but limits are more delicate. The suitable notion of limit turns out to be a kind of lax limit, satisfying certain extra properties.

Of particular interest is the behaviour of the coproduct, both by itself and with respect to partial products. We explore various conditions under which the coproducts are ‘extensive’ in the sense that the total category (of the related partial map category) becomes an extensive category. When partial limits are present, they become ordinary limits in the total category. Thus, when the coproducts are extensive we obtain as the total category a lextensive category. This provides, in particular, a description of the extensive completion of a distributive category.

This paper introduces projective systems for topological and probabilistic event structures. The projective formalism is used for studying the domain of configurations of a prime event structure and its space of maximal elements. This is done from both a topological and a probabilistic viewpoint. We give probability measure extension theorems in this framework.